Big Data bring new opportunities to modern society and challenges to data scientists. On one hand, Big Data hold great promises for discovering subtle population patterns and heterogeneities that are not possible with small-scale data. On the other hand, the massive sample size and high dimensionality of Big Data introduce unique computational and statistical challenges, including scalability and storage bottleneck, noise accumulation, spurious correlation, incidental endogeneity, and measurement errors. These challenges are distinguished and require new computational and statistical paradigm. This article give overviews on the salient features of Big Data and how these features impact on paradigm change on statistical and computational methods as well as computing architectures. We also provide various new perspectives on the Big Data analysis and computation. In particular, we emphasis on the viability of the sparsest solution in high-confidence set and point out that exogeneous assumptions in most statistical methods for Big Data can not be validated due to incidental endogeneity. They can lead to wrong statistical inferences and consequently wrong scientific conclusions.

This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a variable-wise variance and yields selection of better, more robust regressors. Experimental results show superior performance on both simulated and real data sets compared to Leave-One-Out Cross-Validation (LOOCV), kernel-based Information Complexity (ICOMP), and maximum log of marginal likelihood in Gaussian Process Regression (GPR).

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form ${\cal D}(Ku) + \alpha {\cal R} (u) \rightarrow \min_u$ ; where the functional ${\cal D}$ is a data fidelity term also depending on some input data $f$ and measuring the deviation of $Ku$ from such and ${\cal R}$ is a regularization functional. Moreover $K$ is a (often linear) forward operator modeling the dependence of data on an underlying image, and $\alpha$ is a positive regularization parameter. While ${\cal D}$ is often smooth and (strictly) convex, the current practice almost exclusively uses nonsmooth regularization functionals. The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof or $\ell_1$-norms of coefficients arising from scalar products with some frame system. The efficient solution of such variational problems in imaging demands for appropriate algorithms. Taking into account the specific structure as a sum of two very different terms to be minimized, splitting algorithms are a quite canonical choice. Consequently this field has revived the interest in techniques like operator splittings or augmented Lagrangians. Here we shall provide an overview of methods currently developed and recent results as well as some computational studies providing a comparison of different methods and also illustrating their success in applications.

We propose a framework for computer music composition that uses resilient propagation (RProp) and long short term memory (LSTM) recurrent neural network. In this paper, we show that LSTM network learns the structure and characteristics of music pieces properly by demonstrating its ability to recreate music. We also show that predicting existing music using RProp outperforms Back propagation through time (BPTT).

Statistical machine learning methods are increasingly used for neuroimaging data analysis. Their main virtue is their ability to model high-dimensional datasets, e.g. multivariate analysis of activation images or resting-state time series. Supervised learning is typically used in decoding or encoding settings to relate brain images to behavioral or clinical observations, while unsupervised learning can uncover hidden structures in sets of images (e.g. resting state functional MRI) or find sub-populations in large cohorts. By considering different functional neuroimaging applications, we illustrate how scikit-learn, a Python machine learning library, can be used to perform some key analysis steps. Scikit-learn contains a very large set of statistical learning algorithms, both supervised and unsupervised, and its application to neuroimaging data provides a versatile tool to study the brain.

We present a sparse analogue to stochastic gradient descent that is guaranteed to perform well under similar conditions to the lasso. In the linear regression setup with irrepresentable noise features, our algorithm recovers the support set of the optimal parameter vector with high probability, and achieves a statistically quasi-optimal rate of convergence of Op(k log(d)/T), where k is the sparsity of the solution, d is the number of features, and T is the number of training examples. Meanwhile, our algorithm does not require any more computational resources than stochastic gradient descent. In our experiments, we find that our method substantially out-performs existing streaming algorithms on both real and simulated data.

We propose a general technique for improving alternating optimization (AO) of nonconvex functions. Starting from the solution given by AO, we conduct another sequence of searches over subspaces that are both meaningful to the optimization problem at hand and different from those used by AO. To demonstrate the utility of our approach, we apply it to the matrix factorization (MF) algorithm for recommender systems and the coordinate descent algorithm for penalized regression (PR), and show meaningful improvements using both real-world (for MF) and simulated (for PR) data sets. Moreover, we demonstrate for MF that, by constructing search spaces customized to the given data set, we can significantly increase the convergence rate of our technique.

Recent computational strategies based on screening tests have been proposed to accelerate algorithms addressing penalized sparse regression problems such as the Lasso. Such approaches build upon the idea that it is worth dedicating some small computational effort to locate inactive atoms and remove them from the dictionary in a preprocessing stage so that the regression algorithm working with a smaller dictionary will then converge faster to the solution of the initial problem. We believe that there is an even more efficient way to screen the dictionary and obtain a greater acceleration: inside each iteration of the regression algorithm, one may take advantage of the algorithm computations to obtain a new screening test for free with increasing screening effects along the iterations. The dictionary is henceforth dynamically screened instead of being screened statically, once and for all, before the first iteration. We formalize this dynamic screening principle in a general algorithmic scheme and apply it by embedding inside a number of first-order algorithms adapted existing screening tests to solve the Lasso or new screening tests to solve the Group-Lasso. Computational gains are assessed in a large set of experiments on synthetic data as well as real-world sounds and images. They show both the screening efficiency and the gain in terms running times.

This paper addresses how a recursive neural network model can automatically leave out useless information and emphasize important evidence, in other words, to perform "weight tuning" for higher-level representation acquisition. We propose two models, Weighted Neural Network (WNN) and Binary-Expectation Neural Network (BENN), which automatically control how much one specific unit contributes to the higher-level representation. The proposed model can be viewed as incorporating a more powerful compositional function for embedding acquisition in recursive neural networks. Experimental results demonstrate the significant improvement over standard neural models.

This paper studies two important signal processing aspects of equilibrium behavior in non-cooperative games arising in social networks, namely, reinforcement learning and detection of equilibrium play. The first part of the paper presents a reinforcement learning (adaptive filtering) algorithm that facilitates learning an equilibrium by resorting to diffusion cooperation strategies in a social network. Agents form homophilic social groups, within which they exchange past experiences over an undirected graph. It is shown that, if all agents follow the proposed algorithm, their global behavior is attracted to the correlated equilibria set of the game. The second part of the paper provides a test to detect if the actions of agents are consistent with play from the equilibrium of a concave potential game. The theory of revealed preference from microeconomics is used to construct a non-parametric decision test and statistical test which only require the probe and associated actions of agents. A stochastic gradient algorithm is given to optimize the probe in real time to minimize the Type-II error probabilities of the detection test subject to specified Type-I error probability. We provide a real-world example using the energy market, and a numerical example to detect malicious agents in an online social network.